0,2

See also comment for A110047.

Superseeker finds: a(n+1) = 2*A086348(n+1) (A086348's offset is 1: On a 3 X 3 board, number of n-move routes of chess king ending at central cell); binomial transform matches A084159 (Pell oblongs); j-th coefficient of g.f.*(1+x)^j matches A079291 (Squares of Pell numbers); a(n) + a(n+1) = A086346(n+2) (A086346's offset is 1: On a 3 X 3 board, the number of n-move paths for a chess king ending in a given corner cell.)

Recurrence: a(n)=2*a(n-1)+12*a(n-2)+8*a(n-3), where a(1)=1, a(2)=2, a(3)=16; formula a(n)=(1/4)*(-1)^(1-n)*2^n+(1/8)*2^n*(sqrt(2)-1)^(-n)+(1/8)*2^n*(-sqrt(2)-1)^(-n). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 24 2008

seriestolist(series(-1/((2*x+1)*(4*x^2+4*x-1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: -kbasejseq[A*B] with A = + 'i - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and B = - .5'i + .5'j + 'k - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj'

Cf. A084159, A086346, A079291, A110046, A110047, A110049, A110050, A086348.

Sequence in context: A061608 A076616 A127276 this_sequence A094505 A035598 A167566

Adjacent sequences: A110045 A110046 A110047 this_sequence A110049 A110050 A110051

easy,nonn

Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jul 10 2005